Method and apparatus for minimizing optical proximity effects

ABSTRACT

Optical proximity effects (OPEs) are a well-known phenomenon in photolithography. OPEs result from the structural interaction between the main feature and neighboring features. It has been determined by the present inventors that such structural interactions not only affect the critical dimension of the main feature at the image plane, but also the process latitude of the main feature. Moreover, it has been determined that the variation of the critical dimension as well as the process latitude of the main feature is a direct consequence of light field interference between the main feature and the neighboring features. Depending on the phase of the field produced by the neighboring features, the main feature critical dimension and process latitude can be improved by constructive light field interference, or degraded by destructive light field interference. The phase of the field produced by the neighboring features is dependent on the pitch as well as the illumination angle. For a given illumination, the forbidden pitch region is the location where the field produced by the neighboring features interferes with the field of the main feature destructively. The present invention provides a method for determining and eliminating the forbidden pitch region for any feature size and illumination condition. Moreover, it provides a method for performing illumination design in order to suppress the forbidden pitch phenomena, and for optimal placement of scattering bar assist features.

1. FIELD OF THE INVENTION

[0001] The present invention relates to photolithography and moreparticularly to optical proximity correction methods used during thedevelopment of photolithography masks used to manufacture semiconductordevices.

2. BACKGROUND OF THE INVENTION

[0002] Lithographic apparatus can be used, for example, in themanufacture of integrated circuits (ICs). In such a case, the mask willgenerally contain a circuit pattern corresponding to an individual layerof the IC, and a projection beam of radiation will be used to image thispattern onto various target portions (each comprising one or more dies)on a substrate (silicon wafer) that has been coated with a layer ofradiation-sensitive material (resist). In general, a single wafer willcontain a whole network of adjacent target portions that aresuccessively irradiated, one at a time. In one type of lithographicapparatus, each target portion is irradiated by exposing the entire maskpattern onto the target portion in one go; such an apparatus is commonlyreferred to as a wafer stepper. In an alternative apparatus - commonlyreferred to as a step-and-scan apparatus - each target portion isirradiated by progressively scanning the mask pattern through theprojection beam in a given reference direction (the “scanning”direction) while synchronously scanning the substrate parallel oranti-parallel to this direction; in the case of a projection systemhaving a magnification factor M (generally <1), the speed V at which thesubstrate is scanned will be a factor M times that at which the maskpattern is scanned. More information with regard to lithographicapparatus as here described can be gleaned, for example, from U.S. PatNo. 6,046,792, incorporated herein by reference.

[0003] Lithographic apparatus may employ various types of projectionradiation, non-limiting examples of which include ultra-violet light(“UV”) radiation (e.g., with a wavelength of 365 nm, 248 nm, 193 nm, 157nm or 126 nm), extreme UV (“EUV”), X-rays, ion beams or electron beams.Depending on the type of radiation used and the particular designrequirements of the apparatus, it may comprise a projection systemhaving refractive, reflective or catadioptric components, and comprisevitreous elements, grazing-incidence mirrors, selective multi-layercoatings, magnetic and/or electrostatic field lenses, etc; forsimplicity, such components may be loosely referred to in this text,either singly or collectively, as a “lens”.

[0004] In a manufacturing process using such a lithographic projectionapparatus, a pattern in a mask is imaged onto a substrate which is atleast partially covered by a layer of radiation-sensitive material(resist). Prior to this imaging step, the substrate may undergo variousprocedures, such as priming, resist coating and a soft bake. Afterexposure, the substrate may be subjected to other procedures, such as apost-exposure bake (PEB), development, a hard bake andmeasurement/inspection of the imaged features. This array of proceduresis used as a basis to pattern an individual layer of a device, e.g., anintegrated circuit (IC). Such a patterned layer may then undergo variousprocesses such as etching, ion-implantation (doping), metallization,oxidation, chemo-mechanical polishing, etc., all intended to finish offan individual layer. If several layers are required, then the wholeprocedure, or a variant thereof, will have to be repeated for each newlayer. Eventually, an array of devices will be present on the substrate(wafer). These devices are then separated from one another by atechnique such as dicing or sawing, whence the individual devices can bemounted on a carrier, connected to pins, etc. Further informationregarding such processes may be obtained, for example, from the book“Microchip Fabrication: A Practical Guide to Semiconductor Processing”,Third Edition, by Peter van Zant, McGraw Hill Publishing Co., 1997 ISBN0-07-067250-4.

[0005] As semiconductor manufacturing technology is quickly pushingtowards the limits of optical lithography, the state-of-the-artprocesses to date have regularly produced ICs with features exhibitingcritical dimensions (“CDs”) which are below the exposure wavelength(“λ”). A “critical dimension” of a circuit is defined as the smallestwidth of a feature or the smallest space between two features. Forfeature patterns that are designed to be smaller than λ, it has beenrecognized that the optical proximity effect (OPE) becomes much moresevere, and in fact becomes intolerable for leading edge sub-λproduction processes.

[0006] Optical proximity effects are a well known characteristic ofoptical projection exposure tools. More specifically, proximity effectsoccur when very closely spaced circuit patterns are lithographicallytransferred to a resist layer on a wafer. The light waves of the closelyspaced circuit features interact, thereby distorting the finaltransferred pattern features. In other words, diffraction causesadjacent features to interact with each other in such a way as toproduce pattern dependent variations. The magnitude of the OPE on agiven feature depends on the feature's placement on the mask withrespect to other features.

[0007] One of the primary problems caused by such proximity effects isan undesirable variation in feature CDs. For any leading edgesemiconductor process, achieving tight control over the CDs of thefeatures (i.e., circuit elements and interconnects) is typically thenumber one manufacturing goal, since this has a direct impact on wafersort yield and speed-binning of the final product.

[0008] It has been known that the variations in the CDs of circuitfeatures caused by OPE can be reduced by several methods. One suchtechnique involves adjusting the illumination characteristics of theexposure tool. More specifically, by carefully selecting the ratio ofthe numerical aperture of the illumination condenser (“NAc”) to thenumerical aperture of the imaging objective lens (“NAo”) (this ratio hasbeen referred to as the partial coherence ratio-σ), the degree of OPEcan be manipulated to some extent.

[0009] In addition to using relatively incoherent illumination, such asdescribed above, OPE can also be compensated for by “pre-correcting” themask features. This family of techniques is generally known as opticalproximity correction (OPC) techniques.

[0010] For example, in U.S. Pat. No. 5,242,770 (the '770 patent), whichis hereby incorporated by reference, the method of using scattering bars(SBs) for OPC is described. The '770 patent demonstrates that the SBmethod is very effective for modifying isolated features so that thefeatures behave as if the features are dense features. In so doing, thedepth of focus (DOF) for the isolated features is also improved, therebysignificantly increasing process latitude. Scattering bars (also knownas intensity leveling bars or assist bars) are correction features(typically non-resolvable by the exposure tool) that are placed next toisolated feature edges on a mask in order to adjust the edge intensitygradients of the isolated edges. Preferably, the adjusted edge intensitygradients of the isolated edges match the edge intensity gradients-ofthe dense feature edges, thereby causing the SB-assisted isolatedfeatures to have nearly the same width as densely nested features.

[0011] It is generally understood that the process latitude associatedwith dense structures is better than that associated with isolatedstructures under conventional illumination for large feature sizes.However, recently, more aggressive illumination schemes such as annularillumination and multipole illumination have been implemented as a meansof improving resolution. When utilizing such illumination schemes, theinventors of the present invention have noted that some opticalphenomenon have become more prominent. In particular, the inventors havenoticed a forbidden pitch phenomena. More specifically, there are pitchranges within which the process latitude of a “densely located” mainfeature, especially the exposure latitude, is worse than that of anisolated feature of the same size. This important observation indicatesthat the existence of the neighboring feature is not always beneficialfor main feature printing, which is in contradiction to what is commonlyconceived, prior to the discovery by the present inventors. Indeed, thepresent inventors believe that the forbidden pitch phenomenon has becomea limiting factor in advanced photolithography. As such, suppressing theforbidden pitch phenomenon will be necessary to further improve the CDsand process latitude obtainable utilizing currently known semiconductordevice manufacturing tools and techniques.

[0012] Accordingly, the present invention relates to a method andtechnique for identifying and eliminating forbidden pitch regions, whichdegrade the overall printing performance, so as to allow for animprovement of the CDs and process latitude obtainable utilizingcurrently known photolithography tools and techniques.

SUMMARY OF THE INVENTION

[0013] The present invention relates to a method and procedure for bothidentifying “forbidden pitch” regions, in which both the criticaldimension of the feature and the process latitude of the feature arenegatively effected, and eliminating the use of “forbidden pitch”regions during the design/manufacturing process.

[0014] More specifically, the present invention relates to a method ofidentifying undesirable pitches between features when designing anintegrated circuit (or other device) to be formed on a substrate by useof a lithographic exposure tool. In an exemplary embodiment, the methodcomprises the steps of (a) identifying extreme interaction pitch regionsby determining illumination intensity levels for a given illuminationangle over a range of pitches; and (b) identifying the undesirablepitches for each extreme interaction pitch region identified in step (a)by determining illumination intensities for a given extreme interactionpitch region over a range of illumination angles.

[0015] In accordance with the present invention, it is shown that thevariation of the critical dimension as well as the process latitude of amain feature is a direct consequence of light field interference betweenthe main feature and the neighboring features. Depending on the phase ofthe field produced by the neighboring features, the main featurecritical dimension and process latitude can be improved by constructivelight field interference, or degraded by destructive light fieldinterference. The phase of the field produced by the neighboringfeatures can be shown to be dependent on the pitch as well as theillumination angle. For a given illumination angle, the forbidden pitchlies in the location where the field produced by the neighboringfeatures interferes with the field of the main feature destructively.The present invention provides a method for identifying the forbiddenpitch regions (i.e., locations) for any feature size and anyillumination condition. More importantly, the present invention providesa method for performing illumination design in order to suppress theforbidden pitch phenomena, thereby suppressing the negative effectsassociated therewith. In addition, the present invention provides for amethod for utilizing scattering bar placement in conjunction with thesuppression of the forbidden pitch phenomena to further minimize opticalproximity effects and optimize overall printing performance.

[0016] As described in further detail below, the present inventionprovides significant advantages over the prior art. Most importantly,the present invention provides for identifying and eliminating forbiddenpitch regions, which degrade the overall printing performance, therebyallowing for an improvement of the CDs and process latitude obtainableutilizing currently known photolithography tools and techniques.

[0017] Additional advantages of the present invention will becomeapparent to those skilled in the art from the following detaileddescription of exemplary embodiments of the present invention.

[0018] The invention itself, together with further objects andadvantages, can be better understood by reference to the followingdetailed description and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019]FIG. 1a illustrates an exemplary imaging system.

[0020]FIGS. 1b and 1 c illustrate the transformation of an on-axis imagepoint at the exit pupil into a corresponding point in thetwo-dimensional frequency plane.

[0021]FIG. 2 represents an exemplary mask pattern to be printed on awafer.

[0022]FIGS. 3a-3 d illustrate exemplary results of both on-axisillumination and of-axis illumination.

[0023]FIGS. 4a and 4 b illustrate an exemplary interaction between sidefeatures and the main feature at two different pitches under a specificillumination angle.

[0024]FIG. 5 is a graph representing two-dimensional illumination.

[0025]FIG. 6 is a graph representing the conjugated illumination schemerequired for vertical and horizontal feature performance balance.

[0026]FIG. 7 illustrates a flow chart detailing the process ofdefining/identifying the forbidden pitch regions.

[0027]FIG. 8 is a plot resulting from the process of FIG. 7, whichillustrates the extreme interaction pitch regions.

[0028]FIG. 9 illustrates a flow chart detailing the process ofgenerating the illumination map for a given pitch.

[0029]FIGS. 10a-10 c show the illumination maps corresponding to theextreme interaction pitch regions of 480 nm, 560 nm, 635 nm illustratedin FIG. 8, respectively.

[0030]FIG. 10d illustrates the illumination map corresponding to thepitch of 310 nm.

[0031]FIG. 11 illustrates an illumination design that improves theexposure latitude at the 480 nm pitch region while preserving strongconstructive structural interactions at other pitch regions.

[0032]FIG. 12 is a graph illustrating a comparison of the log-slopevalues associated with annular, quadrupole and the modified quadrupoleillumination.

[0033]FIG. 13 shows the extreme interaction edge-to-edge placementpositions of the scattering bars around an isolated main line.

[0034]FIGS. 14a-d are illumination maps generated utilizing quadrupoleillumination for scattering bars having varying separation from a mainfeature.

DETAILED DESCRIPTION OF THE DRAWINGS

[0035] As explained in more detail below, the forbidden pitch phenomenonis a direct consequence of optical interactions between neighboringfeatures. More specifically, the field phase of the neighboring featurerelative to that of the main feature depends on the illumination angleand the separation distance between the features. For a givenillumination angle, there are pitch ranges within which the field phaseproduced by the neighboring feature is 180° out of phase relative to thefield phase of the main feature, thereby resulting in destructiveinterference. Such destructive interference reduces the image contrastof the main feature, and as a result, causes a loss of exposurelatitude. It is these pitch ranges, which cause destructiveinterference, that are referred to as the forbidden pitch ranges, andthat are identified and eliminated by the methods of the presentinvention.

[0036] In accordance with the methods of the present invention, and asexplained in detail below, the forbidden pitch regions (i.e., theextreme structural interaction pitch regions) are mapped out oridentified utilizing an illumination map. In one embodiment, for eachextreme structural interaction pitch, a corresponding illumination mapis obtained, which shows its favorable illumination regions and itsunfavorable illumination regions. As such, by utilizing the illuminationmaps the undesirable forbidden pitch regions can be eliminated.Furthermore, when the neighboring feature size is changed to thescattering bar size, similar constructive and destructive interferenceregions can be located and their corresponding illumination maps canalso be obtained. Based on these illumination maps, the presentinvention also allows for optimal scattering bar placement to bedetermined for a given illumination condition.

[0037] Prior to discussing the details of the present invention, a briefreview of the theory relevant to the method of the present invention ispresented. In accordance with Fourier optics, the imaging process can beviewed as a double diffraction process under coherent illumination. Thelens acts as the Fourier transform device that converts the geometricalinformation of the object (i.e., the reticle) into the spatial frequencyinformation of the object in the frequency domain. The spatial frequencyinformation of the object (i.e., frequency components and theiramplitudes) is displayed at the exit pupil of the optical imagingsystem. If the linear dimensions of the geometrical figures on theobject are much larger than the illumination wavelength, and thetopology of the object is much smaller than the illumination wavelength,then the object can be viewed as purely geometrical and scalardiffraction theory is applicable.

[0038] The foregoing assumptions are currently considered valid for areduction projection optical imaging system with a binary chromereticle. In such cases, the electric field at the exit pupil is relatedto the transmission function of the object through the Fouriertransformation. Although 4× or 5× reduction projection systems areutilized in practical photolithography systems, the following discussionutilizes a 1× system in order to simplify the analysis. The 1× opticalimaging system avoids the complexity of information conversion fromentrance pupil to exit pupil that is required for a 4× or 5× reductionoptical imaging system, namely, the spatial frequency conversion, thefield magnitude conversion and polarization tracking. It is noted,however, that the present invention is equally applicable to othersystems, including a 4× or 5× reduction optical imaging system, or anyother applicable system.

[0039]FIG. 1a illustrates an exemplary imaging system 10 helpful fordescribing the operation of the present invention. As shown, the imagingsystem 10 comprises a monochromatic light source 12, a condenser 14, areticle 16, and a projection lens 18. As also shown, the imaging processgenerates an exit pupil 20 and an image plane 22. In the given system,the illumination scheme is Köhler illumination so that uniformillumination is achieved. Furthermore, if an adjustable aperture stop isplaced at the back focal plane of the projection lens 18, then the backfocal plane becomes the exit pupil because there are no optical elementsbetween the back focal plane and the image plane. When examining theexit pupil from the on-axis image point, each geometrical point at theexit pupil 20 corresponds to a pair of angular coordinates (θ,φ), whichcan be transformed into a corresponding point in the two-dimensionalfrequency plane through the following transformation, described byequation (1) and shown in FIGS. 1b and 1 c.

k_(x)=sinθcosφ, k_(y)=sinθsinφ  (1)

[0040] Now considering an object with a transmission function as shownin FIG. 2, such an object can be treated as a one-dimensional object,with its transmission function expressed as, $\begin{matrix}{{f\left( x_{o} \right)} = {1 - {\left( {1 + \alpha} \right)\left\{ {{r\quad e\quad c\quad {t\left( \frac{x_{o}}{a} \right)}} + {r\quad e\quad c\quad {t\left\lbrack \frac{x_{o} - \left( {b + {a/2} + {c/2}} \right)}{c} \right\rbrack}} + {r\quad e\quad c\quad {t\left\lbrack \frac{x_{o} + \left( {b + {a/2} + {c/2}} \right)}{c} \right\rbrack}}} \right\}}}} & (2)\end{matrix}$

[0041] where $\begin{matrix}{{r\quad e\quad c\quad {t\left( \frac{x_{o}}{a} \right)}} = \left\{ \begin{matrix}{1;} & \left| x_{o} \middle| {< {a/2}} \right. \\{0;} & \left| x_{o} \middle| {> {a/2}} \right.\end{matrix} \right.} & (3)\end{matrix}$

[0042] a is the width of the main feature (the center feature), c is thewidth of the side feature(s) and b is the edge-to-edge separationdistance between the main feature and the side feature. The objectillustrated in FIG. 2 represents a generalized mask pattern. When α=0,it is a binary mask, α=0.06 for a 6% attenuated phase shift mask, anda=1.0 for a chrome-less phase shift mask.

[0043] Under on-axis coherent illumination (sinθ=0) withquasi-monochromatic light source, the field at the exit pupil is$\begin{matrix}{{F\left( k_{x} \right)} \propto {{- \frac{1}{\lambda}}{\int_{- \infty}^{+ \infty}{{f\left( x_{o} \right)}^{{- 2}\pi \quad \quad k_{x}{x_{o}/\lambda}}{x_{o}}}}}} & (4)\end{matrix}$

[0044] where k_(x)=sinθ is the spatial frequency in the frequency planealong the k_(x) axis. It is noted that by a quasi-monochromatic lightsource, it is meant that the coherence length of the light is muchlonger than the optical path difference between any pair of light raysunder consideration. This approximation holds well for light sourcesused in photolithography, especially the KrF excimer light source withits bandwidth less than 1.0 picometer.

[0045]FIGS. 3a-3 d illustrate the results of both on-axis illuminationand off-axis illumination along the x-axis. As shown in FIGS. 3a and 3b, under on-axis illumination, the spectrum of the object is centered.However, under off-axis illumination along the x-axis, as shown in FIGS.3c and 3 d, the spectrum of the object is shifted relative to the exitpupil, and the field at the exit pupil becomes, $\begin{matrix}{{F\left( k_{x} \right)} \propto {{- \frac{i}{\lambda}}{\int_{- \infty}^{+ \infty}{{f\left( x_{o} \right)}^{2\pi \quad i\quad k_{x\quad o}{x_{o}/\lambda}}^{{- 2}\pi \quad i\quad k_{x\quad}{x_{o}/\lambda}}{x_{o}}}}}} & (5)\end{matrix}$

[0046] where k_(xo)=sinθ_(o) and θ_(o) is the illumination angle. Thephase term e^(2πikxoxo/λ) has a simple geometrical interpretation, andaccounts for the phase difference of the illumination field at differentobject points, as illustrated in FIG. 3c.

[0047] By inserting equation (2) into equation (5), the result is:$\begin{matrix}{{F\left( k_{x} \right)} \propto {{\delta \left( {k_{x} - k_{x\quad o}} \right)} - {\left( {1 + \alpha} \right)\left\{ {{\frac{a}{\lambda}\frac{\sin \left\lbrack {\pi \frac{a}{\lambda}\left( {k_{x} - k_{xo}} \right)} \right\rbrack}{\pi \frac{a}{\lambda}\left( {k_{x} - k_{xo}} \right)}} + {^{{- 2}\pi \quad \quad {{p{({k_{x} - k_{x\quad o}})}}/\lambda}}\frac{c}{\lambda}\frac{\sin \left\lbrack {\pi \frac{c}{\lambda}\left( {k_{x} - k_{xo}} \right)} \right\rbrack}{\pi \frac{c}{\lambda}\left( {k_{x} - k_{xo}} \right)}} + {^{2{\pi }\quad {{p{({k_{x} - k_{x\quad o}})}}/\lambda}}\frac{c}{\lambda}\frac{\sin \left\lbrack {\pi \frac{c}{\lambda}\left( {k_{x} - k_{xo}} \right)} \right\rbrack}{\pi \frac{c}{\lambda}\left( {k_{x} - k_{xo}} \right)}}} \right\}}}} & (6)\end{matrix}$

[0048] where p=b+a/2+c/2 is defined as the pitch of the pattern.

[0049] The electric field at the image plane, according to Fourieroptics, is $\begin{matrix}{{g\left( x_{i} \right)} \propto {\frac{1}{\lambda}{\int_{{- N}\quad A}^{{+ N}\quad A}{{F\left( k_{x} \right)}^{2\pi \quad i\quad k_{x}{x_{i}/\lambda}}{k_{x}}}}}} & (7)\end{matrix}$

[0050] It is noted that the quantities set forth in equations (6) and(7) can be rescaled such that all the geometrical dimensions arenormalized to λ/NA, and k_(x) and k_(xo) are normalized to NA.Explicitly, these rescaled quantities can be expressed as,

a _(r) =a·NA/λ, b _(r) =b·NA/λ, c _(r) =c·NA/λ, p _(r) =p·NA/λx _(i)^(r) =x _(i) ·NA/λ, k ^(r) _(x) =k _(x) /NA, k ^(r) _(xo) =k _(xo)/NA=s  (8)

[0051] Using these rescaled quantities, the electric field at the imageplane becomes: $\begin{matrix}{{{g\left( x_{i}^{r} \right)} \propto {^{2{\pi }\quad x_{i}^{r_{s}}} - {\left( {1 + \alpha} \right){\int_{- 1}^{+ 1}{\left\{ {{a_{r}\frac{\sin \left\lbrack {\pi \quad {a_{r}\left( {k_{x}^{r} - s} \right)}} \right\rbrack}{\pi \quad {a_{r}\left( {k_{x}^{r} - s} \right)}}} + {^{{- 2}{{\pi p}_{r}{({k_{x}^{r} - s})}}}c_{r}\frac{\sin \left\lbrack {\pi \quad {c_{r}\left( {k_{x}^{r} - s} \right)}} \right\rbrack}{\pi \quad {c_{r}\left( {k_{x}^{r} - s} \right)}}} + {^{2\pi \quad {{p}_{r}{({k_{x}^{r} - s})}}}c_{r}\frac{\sin \left\lbrack {\pi \quad {c_{r}\left( {k_{x}^{r} - s} \right)}} \right\rbrack}{\pi \quad {c_{r}\left( {k_{x}^{r} - s} \right)}}}} \right\} ^{2{\pi }\quad x_{i}^{r}k_{x}^{r}}{k_{x}^{r}}}}}}}{or}} & (9) \\{{g\left( x_{i}^{r} \right)} \propto {^{2{\pi }\quad x_{i}^{r_{s}}} - {\left( {1 + \alpha} \right){\int_{- 1}^{+ 1}\left\{ {{a_{r}\frac{\sin \left\lbrack {\pi \quad {a_{r}\left( {k_{x}^{r} - s} \right)}} \right\rbrack}{\pi \quad {a_{r}\left( {k_{x}^{r} - s} \right)}}} + {^{2{\pi x}_{i}^{r}k_{x}^{r}}{k_{x}^{r}}} - {\left( {1 + \alpha} \right)^{2\pi \quad {p}_{r}^{s}}{\int_{- 1}^{+ 1}\left\{ {{c_{r}\frac{\sin \left\lbrack {\pi \quad {c_{r}\left( {k_{x}^{r} - s} \right)}} \right\rbrack}{\pi \quad {c_{r}\left( {k_{x}^{r} - s} \right)}}^{2{{\pi }{({x_{i}^{r} - p_{r}})}}k_{x}^{r}\}}{k_{x}^{r}}} - {\left( {1 + \alpha} \right)^{{- 2}\pi \quad {p}_{r}^{s}}{\int_{- 1}^{+ 1}\left\{ {c_{r}\frac{\sin \left\lbrack {\pi \quad {c_{r}\left( {k_{x}^{r} - s} \right)}} \right\rbrack}{\pi \quad {c_{r}\left( {k_{x}^{r} - s} \right)}}^{2{{\pi }{({x_{i}^{r} + p_{r}})}}k_{x}^{r}\}}{k_{x}^{r}}} \right.}}} \right.}}} \right.}}}} & \left( 9^{\prime} \right)\end{matrix}$

[0052] where S is related to the illumination angle. From equation (9′),it is clear that the fields produced by the side features have a phaseterm, e^(=2πip) _(r) ^(s). It is this phase term that plays the centralrole in the determination and elimination of the forbidden pitchregions.

[0053] It is noted that equation (9) or (9′) applies for one-dimensionalillumination. However, as shown below, the two-dimensional illuminationused in photolithography can be approximated as a one-dimensionalillumination for long lines or trench structures.

[0054] As detailed above, it has been determined that under certainillumination conditions there are some pitch regions within which theexposure latitudes of the main feature become very small, even smallerthan that of the isolated feature. Such pitch regions are referred to asforbidden pitch regions, and are caused by destructive interactionbetween the main feature and the side features under those illuminationconditions. Whether the existence of the side features will improve theprocess latitude of the main feature or degrade the process latitude ofthe main feature depends on the fields produced by these side featuresat the main feature Gaussian image point. If the fields of the sidefeatures have the same phases as the field of the main feature at themain feature image location, then constructive interference betweenthese fields can improve the process latitude of the main feature. Ifthe fields of the side features have 180° phase difference with respectto the field of the main feature at the main feature image location,then destructive interference between the fields causes degrading of theprocess latitude for the main feature. The forbidden pitch regions liein the locations where destructive interference occurs under a givenillumination condition. When such situations arise, the process latitudeof the main feature is worse than that of the isolated feature. Sincethe field signs (depending on phases) and their magnitudes from the sidefeatures are determined by the pitch, the illumination angle (s) and thenumerical aperture (NA), constructive and destructive interaction pitchregions can be located using equation (9′). FIGS. 4a and 4 b showexamples of the interaction between side features and the main featureat two different pitches under a specific illumination angle. In thegiven examples, the feature size is 130 nm, NA=0.65, and s=0.4 for abinary mask (α=0). As illustrated in FIG. 4a, at a pitch ofapproximately 470 nm, the minimum intensity of the main feature (dashedline) at its Gaussian image point is higher than that of an isolatedfeature (solid line), leading to a lower image contrast and smallerexposure latitude. As shown in FIG. 4b, at a pitch of approximately 680nm, the minimum intensity of the main feature (dashed line) at itsGaussian image point is lower than that of an isolated feature (solidline), leading to a higher image contrast and larger exposure latitude.

[0055] As noted above, the foregoing analysis of forbidden pitch regionsis based on one-dimensional illumination, i.e. (k_(y)=0). In actuality,the illumination schemes implemented in photolithography aretwo-dimensional. However, for structures that can be approximated asone-dimensional, such as very long lines or trenches, thetwo-dimensional illumination problem can be reduced to a one-dimensionalproblem. The foregoing is illustrated utilizing FIG. 5. Referring toFIG. 5, assuming the structures are infinitely long in the y direction,the Fourier transform spectrum of the structure at the exit pupil willhave zero width in the k_(y) direction. Under this scenario, atwo-dimensional illumination (NA, k_(x), k_(y)) is equivalent to aone-dimensional illumination (NA_(effective), s_(effective)). Therelationship between the two-dimensional illumination and itscorresponding one-dimensional illumination is readily derived,$\begin{matrix}{{{N\quad A_{effective}} = \sqrt{{N\quad A^{2}} - \beta^{2}}}{{s_{effective} = \frac{\alpha}{\sqrt{{N\quad A^{2}} - \beta^{2}}}},{\beta < {N\quad A}}}} & (10)\end{matrix}$

[0056] where NA in equation (10) is the numerical aperture setting inthe employed lithographic projection apparatus.

[0057] Further detailed analysis on the forbidden pitch phenomenon andoptimal illumination design for suppressing forbidden pitch regions hasto take into account the performance balance between “vertical” and“horizontal” features (i.e., features in the y and x direction). Toachieve this performance balance, an illumination source point (α,β) inthe (k_(x)>0, k_(y)>0) illumination space must have a correspondingconjugated illumination source point (−β, α) in the (k_(x),<0, k_(y)>0)illumination space, as shown in FIG. 6. In other words, eachillumination point in the first quadrant exhibits a 90 degree rotationalsymmetry with a corresponding illumination point in the second quadrant.Similarly, in the reduced one-dimensional illumination space, anyillumination source point (NA_(effective), S_(effective)) must have aconjugated illumination point

({square root}{square root over (NA²−NA_(effective) ²S_(effective)²)},−{square root}{square root over (NA²−NA_(effective) ²)}/{squareroot}{square root over (NA²−NA_(effective) ²S_(effective) ²)}).

[0058] Utilizing this conjugated illumination scheme, the forbiddenpitch regions can be identified and eliminated. FIG. 7 illustrates aflow chart detailing the process of defining/identifying the forbiddenpitch regions. The first portion of the process entails determining theinteraction pitch regions for a given (α,β). Referring to FIG. 7, thisis accomplished by utilizing equation 9 or 9′, which as explained aboverepresents the calculation engine associated with one-dimensionalillumination. More specifically, for a given illumination point (i.e.,α, β are fixed), equation 9 or 9′ is utilized to calculate theillumination intensity at a given pitch, I(α, β, pitch) (Step 70). Inaddition, equation 9 or 9′ is utilized to calculate the illuminationintensity of the corresponding 90 degree rotational symmetric point atthe same pitch, I(−β, α, pitch) (Step 72). The two illuminationintensities are then added together (Step 74) to obtain I_(total) (α, β,pitch), and then the log-slope of I_(total) is calculated (Step 76).This process is then repeated for each pitch of interest, I(α, β, pitch)(Steps 78, 80).

[0059]FIG. 8 illustrates a plot of the results of the process of FIG. 7,which depicts the areas having extreme interaction pitch regions.Referring to FIG. 8, the extreme pitch interaction locations areidentified by those areas having a substantial amount of circles. Morespecifically, the extreme pitch interaction locations can be identifiedutilizing the following equation:

d(log-slope of I_(total))/d(pitch)˜0.

[0060] In particular, the locations substantially proximate the locationsatisfying the foregoing equation are extreme pitch interactionlocations. In other words, while the foregoing condition for locatingthe extreme pitch interaction locations specifies a specific location,the actual forbidden pitch is a range around this location. The actualrange is dependent on the wavelength and the NA of the exposureapparatus. From experimental studies, it was determined that theforbidden pitch range around a given specific location is approximately+/−0.12 wavelength/NA. For example, if exposure apparatus utilizes a 248nm source and a NA=0.65, then the extreme interaction pitch range isapproximately +/−45 nm. It is further noted that while the extremeinteraction pitch locations are relatively stable, they are notstationary. Extreme interaction pitch locations can shift slightly withvariations in illumination angle.

[0061] Returning to FIG. 8, it is noted that the example set forth inFIG. 8 was conducted utilizing a set feature size of 130 nm, a scannerNA=0.65, and s effective=0.65. As shown, there are four distinct extremeinteraction pitch regions in the intermediate pitch range (300 nm to 700nm), which are located at approximately 370 nm, 480 nm, 560 nm and 630nm. It is further noted that FIG. 8 does not indicate whether theextreme interaction pitch regions are constructive or destructive, butjust whether or not such regions exist. Also, typically the extremeinteraction pitch regions do not vary with the illumination angle. Theregions tend not to be sensitive to illumination angle.

[0062] Once the extreme interaction pitch regions are identified, thenext portion of the process entails generating illumination maps for thepitches of interest/concern (i.e., the extreme interaction pitchregions). To summarize, for each extreme interaction pitch region, thelog-slope of the main feature image at the mask edge is calculated as afunction of illumination angle. FIG. 9 illustrates a flow chartdetailing the process of generating the illumination map for a givenextreme interaction pitch.

[0063] Referring to FIG. 9, again utilizing equation 9 or 9′, theillumination intensity for a first illumination angle (α, β) and thefixed pitch is calculated (Step 90), and the illumination intensity ofthe corresponding 90 degree rotational symmetric point at the same pitchis calculated (Step 92). The two illumination intensities are then addedtogether (Step 94) to obtain I_(total) (α, β, pitch), and then thelog-slope of I_(total) is calculated (Step 96). This process is thenrepeated for a plurality of illumination angles so as to allow theillumination map to cover at least one quadrant (i.e., 0≦k_(x)≦1,0≦k_(y)≦1), (Steps 98, 100). FIGS. 10a-10 c show the illumination mapscorresponding to the extreme interaction pitch regions of 480 nm, 560nm, 635 nm illustrated in FIG. 8, respectively. FIG. 10d illustrates theillumination map corresponding to the minimum pitch of 310 nm.

[0064] Referring again to FIGS. 10a-10 d, the illumination anglescorresponding to higher values of the log-slope of I_(total) are theillumination angles that provide optimal performance for the givenpitch. In other words, the higher the value of the log-slope ofI_(total), the better the performance. For example, referring to FIG.10a, the optimal illumination angle for this pitch (i.e., 480 nm) isapproximately zero. Any illumination angle corresponding to values ofk_(x)>0.2 and k_(y)>0.2 result in low values of the log-slope ofI_(total), and are therefore undesirable. As shown in FIG. 10a, thehighest values of the log-slope occur when both k_(x) and k_(y) areapproximately zero. Referring to FIG. 10b, the optimal illuminationangles for the 560 nm pitch are angles corresponding approximately toeither k_(x)=0.5 and k_(y)=0, or k_(x)=0 and k_(y)=0.5. Referring toFIG. 10c, the optimal illumination angles for the 635 nm pitch areangles corresponding approximately to k_(x)=0.3 and k_(y)=0.3. Finally,referring to FIG. 10d, the optimal illumination angles for the 310 nmpitch are angles corresponding to either k_(x)=0.5 and k_(y)=0.5.

[0065] Accordingly, from the illumination maps, it is clear that whetheran extreme interaction pitch becomes a forbidden pitch region or afriendly pitch region depends on the illumination employed. Furtherexamination of the illumination maps reveals that the illumination mapat pitch 480 nm is complementary to the illumination maps at 635 nm and310 nm. More specifically, at pitch 480 nm, the desirable illuminationangles correspond to k_(x) and k_(y) equal to approximately zero, andthe undesirable areas correspond to k_(x) and k_(y) equal toapproximately 0.5. Conversely, at pitches of 635 nm and 310 nm, thedesirable illumination angles correspond to k_(x) and k_(y) equal toapproximately 0.5, and the undesirable areas correspond to k_(x) andk_(y) equal to approximately 0. This intrinsic complementary propertyprevents taking advantage of the quadrupole illumination for 130 nm modephotolithography unless there are no structures around 480 nm pitch onthe layer. Analysis of the foregoing illumination maps allows thedesigner to select the illumination angle(s) to be utilized so as tooptimize the printing performance, and more importantly, to avoid theextreme interaction pitch areas which result in destructiveinterference.

[0066] It is noted that the minimum value of the log-slope of I_(total)associated with acceptable performance depends in-part on the resistbeing utilized. For example, different resists exhibit differentcontrasts, which require different minimum values of the log-slope ofI_(total) corresponding to optimal performance regions. As a generalrule, however, a value of the log-slope of I_(total) approximately equalto a greater than 15 results in an acceptable process.

[0067] With regard to optimizing printing performance, referring to theexemplary illumination maps set forth in FIGS. 10a-10 d, it is notedthat in comparison with quadrupole illumination, annular illumination(σ_in=0.55 and σ_out=0.85, for example) can improve image contrastaround the 480 nm pitch region by degrading the image contrast at otherpitch regions. Such an approach reduces the structural interactions atdifferent pitches by averaging the constructive and destructiveinteractions within the illumination space.

[0068] For example, FIG. 11 illustrates an illumination design thatimproves the exposure latitude at the 480 nm pitch region whilepreserving strong constructive structural interactions at other pitchregions. More specifically, FIG. 11 illustrates an illumination designthat provides some illumination at the illumination center since thefavorable illumination for the 480 nm pitch region is around center(k_(x)=0, k_(y)=0). However, the performance balance has to beconsidered when illumination at center is added, because theillumination at the center will unavoidably degrade the image contrastat the minimum pitch region at 310 nm. Comparison of the log-slope usingSolid-C simulation software on annular, quadrupole and the modifiedquadrupole illumination (σ_center=0.15 and σ_center=0.2) is shown inFIG. 12. The features are 130 nm lines on a 6% attenuated phase shiftmask. As shown from the simulation results, the modified quadrupole withcenter σ=0.2 will provide an overall better process, and it also allowstaking full advantage of the assist feature benefits.

[0069] It is noted that the term QUASAR used in the figures refers tothe generation of quadrupole illumination using a Diffractive OpticalElement (DOE), which re-distributes incoming radiation flux rather thanblocking/passing it. In particular, 30-degree QUASAR refers to aquadrupole pattern in which the 4 poles are segments of an annulus, andeach subtends an angle of 30 degrees with the center of the annulus.

[0070] It is also possible to utilize the foregoing illumination maps toassist in the placement of scattering bars, which operate to mitigateoptical proximity effects. The use of such scattering bars has beendescribed in U.S. Pat. No. 5,242,770 noted above. As detailed in the'770 patent, it is has been known that adding assist features aroundsparse (e.g. isolated) features is necessary for aggressive printing inphotolithography in order to achieve a manufacturable process. However,the placements of such assist features are very critical for achievingthe optimal and desired effect. More specifically, similar to adjacentfeatures, it is possible for incorrect placement of scattering barsaround the main feature to degrade the process latitude of the mainfeature. For example, if the scattering bar is placed in a forbiddenpitch region. Accordingly, the present invention can also be utilizedfor the placement of scattering bars so as to assure that the scatteringbars are not positioned in a forbidden pitch region for a givenillumination angle.

[0071] The implementation of scattering bar technology involves thedetermination of scattering bar size and placement. Although the largestscattering bar size should be used within the resist contrastcapability, the practical design has to take other factors into account,such as the dimension errors of scattering bars resulting from themask-making process. Current scattering bar size is typically around60-80 nm. The scattering bar placement is mainly based on the placementrules that are developed from experiments, using a specially designedreticle such as MaskTools's LINESWEEPER™ reticle. The principle ofscattering bar placement is similar to that of forbidden pitch phenomenadescribed above.

[0072] More specifically, the first step entails identifying the extremeinteraction locations between the scattering bars and the main features.The process for identifying the extreme interaction locations issubstantially the same as the process described above for identifyingthe extreme interaction pitch regions. However, instead of identifyingsmall log-slope regions as is necessary for identification of forbiddenpitch regions, regions that show large log-slope for the main featureare identified. FIG. 13 shows the extreme interaction edge-to-edgeplacement positions of the scattering bars around an isolated main line.As shown, these extreme edge-to-edge positions are around 235 nm, 375nm, 510 nm, 655 nm, etc.

[0073] Once the extreme interaction locations are identified, the nextstep is to select the ones that have a similar illumination map to theillumination conditions already selected for the process. It is notedthat it is not always true that the closer the scattering bar is placedaround the main isolated feature the better, since each placementposition has its own favorable illumination region. FIGS. 14a-d areillumination maps generated for quadrupole illumination for scatteringbars having varying separation from the main feature. Referring to FIGS.14a-14 d, strong scattering bar effects are expected when scatteringbars are placed around 235 nm or 510 nm. However, improper placement ofscattering bars around 375 nm or 650 nm will degrade the image contrastof the main isolated feature under quadrupole illumination. If space isprovided around the sparse features, a second pair of scattering barscan be added. When annular illumination is utilized, constructive anddestructive structural interactions from scattering bars will beaveraged out to some degree, and the benefit from the assist features istherefore greatly reduced. Thus, it is clear from the foregoing thatplacement of scattering bars is strongly dependent on the illuminationchosen. It is also noted that when multiple scattering bars arerequired, their illumination maps should belong to the same class (i.e.,the illumination maps should be similar).

[0074] To summarize, because both the forbidden pitch phenomena and thescattering bar technology are a direct consequence of opticalinteractions between neighboring features, they can be treated andunderstood under a unified framework. The foregoing makes clear that thefield phase of the neighboring feature relative to that of the mainfeature depends on the illumination and the separation distance. For agiven illumination angle, there are pitch ranges within which the fieldphase produced by the neighboring feature is 180° out of phase relativeto the field phase of the main feature, resulting in destructiveinterference. Such destructive interference reduces the image contrastof the main feature, and therefore causes a loss of exposure latitude.The forbidden pitch regions, or more precisely the extreme structuralinteraction pitch regions, can easily be mapped out and determined asdetailed above. For each extreme structural interaction pitch, acorresponding illumination map can be obtained, which shows itsfavorable illumination regions and its unfavorable illumination regions.The illumination maps are then utilized as a reference for illuminationdesign. When the neighboring feature size is changed to the scatteringbar size, similar constructive and destructive interference regions canbe located and their corresponding illumination maps can also beobtained. Based on these illumination maps, the optimal scattering barplacement can be determined for a given illumination condition. Thus, ingeneral, scattering bars should be placed at the pitch regions wherefields from scattering bars are in phase with the field from the mainfeature at the main feature Gaussian image point under a givenillumination condition. When the illumination scheme utilized ischanged, the scattering bar placements should be adjusted accordingly.When multiple scattering bars are required, their illumination mapsshould have similarity to achieve maximum benefit.

[0075] Although specific reference may be made in this text to the useof the apparatus according to the invention in the manufacture of ICs,it should be explicitly understood that such an apparatus has many otherpossible applications. For example, it may be employed in themanufacture of integrated optical systems, guidance and detectionpatterns for magnetic domain memories, liquid-crystal display panels,thin-film magnetic heads, etc. The skilled artisan will appreciate that,in the context of such alternative applications, any use of the terms“reticle”, “wafer” or “die” in this text should be considered as beingreplaced by the more general terms “mask”, “substrate” and “targetportion”, respectively.

[0076] Although this text has concentrated on lithographic apparatus andmethods whereby a mask is used to pattern the radiation beam enteringthe projection system, it should be noted that the invention presentedhere should be viewed in the broader context of lithographic apparatusand methods employing generic “patterning means” to pattern the saidradiation beam. The term “patterning means” as herein employed refersbroadly to means that can be used to endow an incoming radiation beamwith a patterned cross-section, corresponding to a pattern that is to becreated in a target portion of the substrate; the term “light valve” hasalso been used in this context. Generally, the said pattern willcorrespond to a particular functional layer in a device being created inthe target portion, such as an integrated circuit or other device.Besides a mask on a mask table, such patterning means include thefollowing exemplary embodiments.

[0077] A programmable mirror array. An example of such a device is amatrix-addressable surface having a viscoelastic control layer and areflective surface. The basic principle behind such an apparatus is that(for example) addressed areas of the reflective surface reflect incidentlight as diffracted light, whereas unaddressed areas reflect incidentlight as undiffracted light. Using an appropriate filter, the saidundiffracted light can be filtered out of the reflected beam, leavingonly the diffracted light behind; in this manner, the beam becomespatterned according to the addressing pattern of the matrix-addressablesurface. The required matrix addressing can be performed using suitableelectronic means. More information on such mirror arrays can be gleaned,for example, from U.S. Pat. Nos. 5,296,891 and 5,523,193, which areincorporated herein by reference.

[0078] Another example of such a device is a programmable LCD array. Anexample of such a construction is given in U.S. Pat. No. 5,229,872,which is incorporated herein by reference.

[0079] As described above, the method of the present invention providessignificant advantages over the prior art. Most importantly, the presentinvention provides for identifying and eliminating forbidden pitchregions, which degrade the overall printing performance, therebyallowing for an improvement of the CDs and process latitude obtainableutilizing currently known photolithography tools and techniques.

[0080] Although certain specific embodiments of the present inventionhave been disclosed, it is noted that the present invention may beembodied in other forms without departing from the spirit or essentialcharacteristics thereof. The present embodiments are therefor to beconsidered in all respects as illustrative and not restrictive, thescope of the invention being indicated by the appended claims, and allchanges that come within the meaning and range of equivalency of theclaims are therefore intended to be embraced therein.

1. A method of identifying an extreme interaction pitch region whendesigning a mask for transferring a lithographic pattern correspondingto an integrated device from said mask onto a substrate by use of alithographic apparatus, said method comprising the steps of: (a)determining an illumination intensity for a first pitch and a firstillumination angle, (b) determining an illumination intensity for saidfirst pitch and a second illumination angle, said second illuminationangle being rotationally symmetric with respect to said firstillumination angle, (c) determining a total illumination intensity forsaid first pitch by combining the illumination intensity associated withsaid first illumination angle and said second illumination angle, (d)determining the log-slope of said total illumination intensity, and (e)identifying said first pitch as an extreme interaction pitch region ifthe value of the derivative of the log-slope of said total illuminationintensity divided by the derivative of said first pitch is approximatelyequal to zero.
 2. The method of identifying an extreme interaction pitchregion according to claim 1, further comprising the steps of: repeatingsteps (a)-(e) for a plurality of different pitches.
 3. The method ofidentifying an extreme interaction pitch region according to claim 2,wherein said extreme interaction pitch regions are substantiallyindependent of said illumination angle.
 4. The method of identifying anextreme interaction pitch region according to claim 1, wherein saidsecond illumination angle exhibits a 90 degree rotational symmetry withrespect to said first illumination angle.
 5. The method of identifyingan extreme interaction pitch region according to claim 2, furthercomprising the steps of: for a given extreme interaction pitch: (f)determining an illumination intensity for said given extreme interactionpitch and a first illumination angle, (g) determining an illuminationintensity for said given extreme interaction pitch and a secondillumination angle, said second illumination angle being rotationallysymmetric with respect to said first illumination angle, (h) determininga second total illumination intensity for said given extreme interactionpitch by combining the illumination intensity associated with said firstillumination angle and said second illumination angle, (i) determiningthe log-slope of said second total illumination intensity, (j) repeatingsteps (f)-(i) for a plurality of different illumination angles, and (k)identifying a given illumination angle as corresponding to anundesirable pitch region if said log-slope of said second totalillumination intensity exceeds a predetermined value.
 6. A method ofidentifying undesirable pitches between features when designing anintegrated device to be formed on a substrate by use of a lithographicapparatus, said method comprising the steps of: (a) determining anillumination intensity for a first pitch and a first illumination angle,(b) determining an illumination intensity for said first pitch and asecond illumination angle, said second illumination angle beingrotationally symmetric with respect to said first illumination angle,(c) determining a total illumination intensity for said first pitch bycombining the illumination intensity associated with said firstillumination angle and said second illumination angle, (d) determiningthe log-slope of said total illumination intensity, (e) identifying saidfirst pitch as an extreme interaction pitch if the value of thederivative of the log-slope of said total illumination intensity dividedby the derivative of said first pitch is approximately equal to zero,and (f) repeating steps (a)-(e) for a plurality of different pitches;wherein for each extreme interaction pitch identified in steps (a)-(f):(g) an illumination intensity is determined for said given extremeinteraction pitch and said first illumination angle, (h) an illuminationintensity is determined for said given extreme interaction pitch andsaid second illumination angle, (i) a second total illuminationintensity is determined for said given extreme interaction pitch bycombining the illumination intensity associated with said firstillumination angle and said second illumination angle, (j) the log-slopeof said second total illumination intensity is determined, (k) steps(g)-(j) are repeated for a plurality of different illumination angles,and (l) a given illumination angle is identified as corresponding to anundesirable pitch region if said log-slope of said second totalillumination intensity exceeds a predetermined value.
 7. The method ofidentifying undesirable pitches between features according to claim 6,wherein said second illumination angle exhibits a 90 degree rotationalsymmetry with said first illumination angle.
 8. A method of identifyingundesirable pitches between features when designing an integrated deviceto be formed on a substrate by use of a lithographic apparatus, saidmethod comprising the steps of: (a) identifying extreme interactionpitch regions by determining illumination intensity levels for a givenillumination angle over a range of pitches; and (b) identifying saidundesirable pitches for each extreme interaction pitch region identifiedin step (a) by determining illumination intensities for a given extremeinteraction pitch region over a range of illumination angles.
 9. Themethod of identifying undesirable pitches between features according toclaim 8, wherein said extreme interaction pitch regions define regionswhich exhibit either substantial constructive optical interference orsubstantial destructive optical interference.
 10. The method ofidentifying undesirable pitches between features according to claim 8,wherein said undesirable pitches have corresponding illuminationintensities exceeding a predetermined value.
 11. A method of identifyingundesirable pitches between a feature and an optical proximitycorrection element when designing an integrated device to be formed on asubstrate by use of a lithographic apparatus, said method comprising thesteps of: (a) identifying extreme interaction pitch regions bydetermining illumination intensity levels for a given illumination angleover a range of pitches; and (b) identifying said undesirable pitchesfor each extreme interaction pitch region identified in step (a) bydetermining illumination intensities for a given extreme interactionpitch region over a range of illumination angles.
 12. The method ofidentifying undesirable pitches between features according to claim 11,wherein said extreme interaction pitch regions define regions whichexhibit either substantial constructive optical interference orsubstantial destructive optical interference.
 13. The method ofidentifying undesirable pitches between features according to claim 10,wherein said undesirable pitches have corresponding illuminationintensities exceeding a predetermined value.